Final answer to the problem
Step-by-step Solution
Specify the solving method
Divide $x^2+1$ by $x^2-1$
Learn how to solve integrals of rational functions problems step by step online.
$\begin{array}{l}\phantom{\phantom{;}x^{2}-1;}{\phantom{;}1\phantom{;}\phantom{;}}\\\phantom{;}x^{2}-1\overline{\smash{)}\phantom{;}x^{2}\phantom{-;x^n}+1\phantom{;}\phantom{;}}\\\phantom{\phantom{;}x^{2}-1;}\underline{-x^{2}\phantom{-;x^n}+1\phantom{;}\phantom{;}}\\\phantom{-x^{2}+1\phantom{;}\phantom{;};}\phantom{;}2\phantom{;}\phantom{;}\\\end{array}$
Learn how to solve integrals of rational functions problems step by step online. Find the integral int((x^2+1)/(x^2-1))dx. Divide x^2+1 by x^2-1. Resulting polynomial. Expand the integral \int\left(1+\frac{2}{x^2-1}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. We can solve the integral \int\frac{2}{x^2-1}dx by applying integration method of trigonometric substitution using the substitution.